Overview

In 1913 a letter containing 120 astonishing theorems arrived at Cambridge; its author was an unknown Indian clerk who had never attended university. Within a decade Srinivasa Ramanujan had rediscovered the most advanced results of European analysis and pushed far beyond them, forging identities that mathematicians still mine today. Working alone on a slate in Madras, he filled three notebooks with 3,900 results—nearly all proven correct a century later—while revolutionizing partition theory, mock theta functions, and infinite series for π.

Ramanujan’s blend of intuition and computation is legendary: he once declared that every positive integer is “a personal friend,” then stunned G. H. Hardy by instantly recalling 1729 as the smallest number expressible as a sum of two cubes in two distinct ways. His formulas have found unexpected homes in string theory, crystallography, and RSA cryptography, making him one of the most cited mathematicians of the 20th century despite his death at 32.

Background & Origins

Born 22 December 1887 in Erode, Tamil Nadu, Ramanujan grew up in a modest Iyengar Brahmin household. A precocious child, he mastered primary arithmetic by age 7 and began reinventing mathematics at 13, when a library copy of G. S. Carr’s Synopsis of Pure Mathematics became his only textbook. The book’s 5,000 theorems—presented without proofs—taught him to think synthetically, a habit that later dazzled and frustrated his Cambridge mentors.

In 1903 he entered Government Arts College, Kumbakonam, but lost his scholarship the next year for neglecting every subject except mathematics. Marriage to 9-year-old Janaki Ammal in 1909 forced him to seek employment; he secured a low-paid clerkship at the Madras Port Trust in 1912, scribbling theorems on loose sheets that colleagues secretly forwarded to university professors.

Major Achievements & Milestones

Infinite Series for 1/π (1914): Ramanujan produced 14 rapidly converging series, one of which doubles the number of correct digits at every step. The Chudnovsky brothers used his blueprint in 1989 to compute π to a then-world-record 2 billion digits.

Partition Formula (1918): He and Hardy derived the first exact formula for p(n), the number of ways to write n as a sum of positive integers. Before this, mathematicians could only guess; overnight, partitions became computable for numbers like p(200) = 3,972,999,029,388.

Mock Theta Functions (1920): On his deathbed he introduced functions that behave like modular forms but lack their symmetry. These “mock thetas” were finally understood in 2002 by Zwegers, and now count black-hole micro-states in AdS/CFT correspondence.

Timeline

- 1887: Born in Erode, Madras Presidency, British India
- 1903: Matriculates from Town Higher Secondary School with perfect math marks
- 1912: Publishes first paper—on Bernoulli numbers—in Journal of the Indian Mathematical Society
- 1914: Sails to England, begins five-year collaboration with G. H. Hardy at Trinity College, Cambridge
- 1916: Awarded Bachelor of Science by Research (later renamed PhD) for his thesis on highly composite numbers
- 1918: Elected Fellow of the Royal Society (FRS)—second Indian and youngest Fellow at 30
- 1919: Returns to India in ill health; elected first Indian Fellow of Trinity College
- 1920: Dies 26 April in Chetput, Madras, aged 32

Impact & Legacy

Ramanujan’s notebooks—once dismissed as “mystical scribbles”—have become algorithmic gold mines. The Ramanujan τ-function, a cornerstone of modular-form theory, underpins the proof of Fermat’s Last Theorem. His Lost Notebook, rediscovered in 1976, contained 600 unproven identities; proving them has spawned 3,000 research papers and two Fields Medals (1998, 2018). India celebrates National Mathematics Day on his birthday, and the Ramanujan Journal (founded 1997) is devoted to areas he influenced. NASA’s Ramanujan supercomputer and the lunar crater Ramanujan immortalize a man who turned intuition into universal truth.

Records & Notable Facts

- Fastest rise to Royal Society Fellow in mathematics history—just 4 years after leaving India
- Only mathematician to have both a journal and a planetoid (asteroid 4130 Ramanujan) named after him during the 20th century
- His notebooks contain 3,900 results; fewer than 20 have been proven false
- The 2015 film The Man Who Knew Infinity brought his story to 30 million viewers worldwide

> “An equation for me has no meaning unless it expresses a thought of God.”
> — Srinivasa Ramanujan, in a letter to G. H. Hardy, 1914